Can the position of an adjective be used to determine the noun it applies to?

Given the sentence: "A mother beat up her daughter because she was drunk".

Is there a grammar rule that can help resolve the ambiguity of whether "drunk" refers to the mother or the daughter?

Update: The question isn't about how to rewrite the sentence. If you found the sentence already written and had no access to the author in order to sort out the ambiguity, what would be the most correct interpretation?

A mother beat up her daughter because she was drunk.

To solve the ambiguity:

• A drunk mother beat up her daughter.
• A mother beat up her drunk daughter.

It hardly seems necessary to add the because clause, given the context that one or the other's drunkenness was obviously the cause of the action, since no other reason is given for it.

But if you must include the modifying clause:

• Because a mother was drunk, she beat up her daughter.
• Because the daughter was drunk, her mother beat her up.